Using the steps below, you are going to show that in the Hotelling model the optimal...

 

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Using the steps below, you are going to show that in the Hotelling model the optimal configura- tion of firms (from the benevolent social planner's/technocrat's perspective) is at a = 1, b = 14. 3 1. What is the total surplus (consumer surplus + producer surplus) generated by a purchase from consumer x at firm A? firm B? 2. Using what you found in 1, show that is socially optimal (total surplus is maximized) for x to purchase from A if t. (a-x)2 t (1-b - x). = 3. Assume a symmetric equilibrium where a b. Part 2 shows that is socially optimal for consumer x to purchase from the store that minimizes his individual travel costs. Likewise, the social planner would like to choose a that minimizes city-wide travel costs. Use inte- gration to find the total travel costs over all x. (Hint: It is save to assume that a stays in the interval [0,2]) 4. Show that the a that minimizes the total travel costs is a = 5. Discuss how the free market generates "too much" product differentiation in the Hotelling model. Using the steps below, you are going to show that in the Hotelling model the optimal configura- tion of firms (from the benevolent social planner's/technocrat's perspective) is at a = 1, b = 14. 3 1. What is the total surplus (consumer surplus + producer surplus) generated by a purchase from consumer x at firm A? firm B? 2. Using what you found in 1, show that is socially optimal (total surplus is maximized) for x to purchase from A if t. (a-x)2 t (1-b - x). = 3. Assume a symmetric equilibrium where a b. Part 2 shows that is socially optimal for consumer x to purchase from the store that minimizes his individual travel costs. Likewise, the social planner would like to choose a that minimizes city-wide travel costs. Use inte- gration to find the total travel costs over all x. (Hint: It is save to assume that a stays in the interval [0,2]) 4. Show that the a that minimizes the total travel costs is a = 5. Discuss how the free market generates "too much" product differentiation in the Hotelling model.